Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n = int(input())

k = int(math.sqrt(2*n))

check = False

for i in range(k, 0, -1):
    p = n - i*(i+1)//2
    if p <= 0:
        continue

    sqrt_p = int(math.sqrt(2*p))

    if sqrt_p*(sqrt_p + 1)//2 == p:
        check = True
        break

if check:
    print("YES")
else:
    print("NO")